Subgroups — C₂×C₁₀₁×#1907 #38803152

Order 25856.

1826 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#131×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#100×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#1907	C₂	1	8	yes	maximal, direct product factor
7	C₂×#343×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#341×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	4	no	—
12	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
13	C₂×AGL(1,ℤ/8)×C₁₀₁	C₄	1	8	yes	complemented
14	C₂×AGL(1,ℤ/8)×C₁₀₁	C₂²	1	4	yes	—
15	C₂²×SD₁₆×C₁₀₁	—	2	1	no	—
16	C₂²×D₈×C₁₀₁	—	2	1	no	—
17	C₂×#131×C₁₀₁	—	2	4	no	—
18	C₂×#131×C₁₀₁	—	2	4	no	—
19	C₂×#131×C₁₀₁	—	2	2	no	—
20	C₂×#131×C₁₀₁	C₂²	1	4	yes	complemented
21	C₂²×M₁₆×C₁₀₁	—	2	1	no	—
22	C₂²×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₁₀₁	—	2	1	no	—
26	C₂³×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
28	#417×C₁₀₁	—	2	2	no	—
29	#417×C₁₀₁	C₂²	1	4	yes	complemented
30	C₂×#103×C₁₀₁	—	2	1	no	—
31	C₂×#102×C₁₀₁	—	2	1	no	—
32	C₂×#102×C₁₀₁	—	2	1	no	—
33	C₂×#102×C₁₀₁	—	2	1	no	—
34	C₂×#102×C₁₀₁	—	2	2	no	—
35	C₂×#102×C₁₀₁	C₂²	1	4	yes	complemented
36	C₂×#100×C₁₀₁	—	2	4	no	—
37	C₂×#100×C₁₀₁	C₂²	1	4	yes	complemented
38	#343×C₁₀₁	C₂²	1	4	yes	complemented
39	#341×C₁₀₁	C₂²	1	4	yes	complemented
40	C₂⁵×C₁₀₁	—	2	1	no	—
41	C₂×#41×C₁₀₁	—	2	2	no	—
42	C₂×#41×C₁₀₁	—	2	1	no	—
43	C₂×#41×C₁₀₁	—	2	2	no	—
44	C₂×#41×C₁₀₁	—	2	1	no	—
45	C₂×#41×C₁₀₁	C₂×C₄	1	4	yes	—
46	C₂×#41×C₁₀₁	D₄	1	4	yes	—
47	C₂×#41×C₁₀₁	D₄	1	2	yes	—
48	C₂×#41×C₁₀₁	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₀₁	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₀₁	—	2	1	no	—
51	C₂²×D₄×C₁₀₁	—	2	1	no	—
52	C₂²×D₄×C₁₀₁	—	2	1	no	—
53	C₂²×D₄×C₁₀₁	—	2	1	no	—
54	C₂²×D₄×C₁₀₁	—	2	2	no	—
55	C₂²×D₄×C₁₀₁	—	2	1	no	—
56	C₂²×D₄×C₁₀₁	—	2	2	no	—
57	C₂²×D₄×C₁₀₁	—	2	2	no	—
58	C₂²×D₄×C₁₀₁	—	2	1	no	—
59	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
60	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₀₁	—	2	1	no	—
63	C₂³×C₄×C₁₀₁	—	2	1	no	—
64	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	AGL(1,ℤ/8)×C₁₀₁	—	2	16	no	—
66	AGL(1,ℤ/8)×C₁₀₁	—	2	8	no	—
67	AGL(1,ℤ/8)×C₁₀₁	C₂×C₄	1	16	yes	complemented
68	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
69	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
70	C₂×D₈×C₁₀₁	—	2	8	no	—
71	C₂×D₈×C₁₀₁	—	2	4	no	—
72	#131×C₁₀₁	—	2	16	no	—
73	#131×C₁₀₁	—	2	8	no	—
74	#131×C₁₀₁	—	2	8	no	—
75	C₂×M₁₆×C₁₀₁	—	2	8	no	—
76	C₂×M₁₆×C₁₀₁	—	2	2	no	—
77	C₂×M₁₆×C₁₀₁	—	2	1	no	—
78	C₂×M₁₆×C₁₀₁	—	2	2	no	—
79	C₂×M₁₆×C₁₀₁	—	2	1	no	—
80	C₂×M₁₆×C₁₀₁	—	2	1	no	—
81	C₂×M₁₆×C₁₀₁	—	2	4	no	—
82	C₂×M₁₆×C₁₀₁	—	2	2	no	—
83	C₂×M₁₆×C₁₀₁	—	2	2	no	—
84	C₂×M₁₆×C₁₀₁	C₂×C₄	1	4	yes	—
85	C₂×M₁₆×C₁₀₁	D₄	1	4	yes	—
86	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
87	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
88	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
89	C₂²×C₈×C₁₀₁	—	2	8	no	—
90	C₂²×C₈×C₁₀₁	—	2	1	no	—
91	C₂²×C₈×C₁₀₁	—	2	2	no	—
92	C₂²×C₈×C₁₀₁	—	2	2	no	—
93	C₂²×C₈×C₁₀₁	—	2	1	no	—
94	C₂²×C₈×C₁₀₁	—	2	4	no	—
95	C₂²×C₈×C₁₀₁	—	2	1	no	—
96	C₂²×C₈×C₁₀₁	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₁₀₁	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
99	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
106	#103×C₁₀₁	—	2	4	no	—
107	#102×C₁₀₁	—	2	4	no	—
108	#102×C₁₀₁	—	2	4	no	—
109	#102×C₁₀₁	—	2	4	no	—
110	#100×C₁₀₁	—	2	8	no	—
111	C₂⁴×C₁₀₁	—	2	1	no	—
112	C₂⁴×C₁₀₁	—	2	4	no	—
113	C₂⁴×C₁₀₁	—	2	2	no	—
114	C₂⁴×C₁₀₁	—	4	1	no	—
115	C₂⁴×C₁₀₁	—	4	1	no	—
116	C₂⁴×C₁₀₁	—	4	2	no	—
117	C₂⁴×C₁₀₁	—	8	2	no	—
118	C₂⁴×C₁₀₁	—	8	2	no	—
119	C₂⁴×C₁₀₁	#41	1	1	yes	characteristic
120	#41×C₁₀₁	—	2	4	no	—
121	#41×C₁₀₁	—	2	4	no	—
122	#41×C₁₀₁	—	2	4	no	—
123	#41×C₁₀₁	—	2	4	no	—
124	#41×C₁₀₁	—	2	4	no	—
125	#41×C₁₀₁	—	2	2	no	—
126	#41×C₁₀₁	—	2	2	no	—
127	#41×C₁₀₁	C₂²⋊C₄	1	8	yes	—
128	#41×C₁₀₁	C₂²×C₄	1	4	yes	—
129	#41×C₁₀₁	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₁₀₁	—	2	1	no	—
131	C₂×Q₈×C₁₀₁	—	2	2	no	—
132	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	4	yes	—
133	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₀₁	—	2	4	no	—
135	C₂×D₄×C₁₀₁	—	2	2	no	—
136	C₂×D₄×C₁₀₁	—	2	4	no	—
137	C₂×D₄×C₁₀₁	—	2	2	no	—
138	C₂×D₄×C₁₀₁	—	2	4	no	—
139	C₂×D₄×C₁₀₁	—	2	4	no	—
140	C₂×D₄×C₁₀₁	—	2	4	no	—
141	C₂×D₄×C₁₀₁	—	2	4	no	—
142	C₂×D₄×C₁₀₁	—	2	4	no	—
143	C₂×D₄×C₁₀₁	—	2	2	no	—
144	C₂×D₄×C₁₀₁	—	2	1	no	—
145	C₂×D₄×C₁₀₁	—	2	2	no	—
146	C₂×D₄×C₁₀₁	—	2	2	no	—
147	C₂×D₄×C₁₀₁	—	2	2	no	—
148	C₂×D₄×C₁₀₁	—	2	2	no	—
149	C₂×D₄×C₁₀₁	—	2	2	no	—
150	C₂×D₄×C₁₀₁	—	4	2	no	—
151	C₂×D₄×C₁₀₁	—	4	2	no	—
152	C₂×D₄×C₁₀₁	—	4	2	no	—
153	C₂×D₄×C₁₀₁	—	4	2	no	—
154	C₂×D₄×C₁₀₁	—	4	1	no	—
155	C₂×D₄×C₁₀₁	—	4	1	no	—
156	C₂×D₄×C₁₀₁	—	4	2	no	—
157	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
158	C₂×D₄×C₁₀₁	C₂²×C₄	1	4	yes	—
159	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₀₁	—	2	1	no	—
161	C₂²×C₄×C₁₀₁	—	2	4	no	—
162	C₂²×C₄×C₁₀₁	—	2	4	no	—
163	C₂²×C₄×C₁₀₁	—	2	2	no	—
164	C₂²×C₄×C₁₀₁	—	2	2	no	—
165	C₂²×C₄×C₁₀₁	—	2	2	no	—
166	C₂²×C₄×C₁₀₁	—	4	1	no	—
167	C₂²×C₄×C₁₀₁	—	4	1	no	—
168	C₂²×C₄×C₁₀₁	—	8	2	no	—
169	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
177	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
178	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
179	SD₁₆×C₁₀₁	—	2	16	no	—
180	D₈×C₁₀₁	—	2	16	no	—
181	M₁₆×C₁₀₁	—	2	16	no	—
182	M₁₆×C₁₀₁	—	2	4	no	—
183	M₁₆×C₁₀₁	—	2	4	no	—
184	M₁₆×C₁₀₁	—	2	2	no	—
185	M₁₆×C₁₀₁	—	2	2	no	—
186	M₁₆×C₁₀₁	—	2	2	no	—
187	M₁₆×C₁₀₁	—	2	2	no	—
188	M₁₆×C₁₀₁	—	4	2	no	—
189	M₁₆×C₁₀₁	C₂²×C₄	1	4	yes	—
190	M₁₆×C₁₀₁	C₂×D₄	1	4	yes	—
191	C₂×C₈×C₁₀₁	—	2	16	no	—
192	C₂×C₈×C₁₀₁	—	2	4	no	—
193	C₂×C₈×C₁₀₁	—	2	2	no	—
194	C₂×C₈×C₁₀₁	—	2	4	no	—
195	C₂×C₈×C₁₀₁	—	2	2	no	—
196	C₂×C₈×C₁₀₁	—	2	4	no	—
197	C₂×C₈×C₁₀₁	—	2	2	no	—
198	C₂×C₈×C₁₀₁	—	2	2	no	—
199	C₂×C₈×C₁₀₁	—	2	2	no	—
200	C₂×C₈×C₁₀₁	—	2	2	no	—
201	C₂×C₈×C₁₀₁	—	2	2	no	—
202	C₂×C₈×C₁₀₁	—	4	2	no	—
203	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
204	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₁₀₁	—	2	2	no	—
206	C₄⋊C₄×C₁₀₁	—	2	2	no	—
207	C₄⋊C₄×C₁₀₁	—	4	1	no	—
208	C₄⋊C₄×C₁₀₁	—	4	1	no	—
209	C₂³×C₁₀₁	—	2	2	no	—
210	C₂³×C₁₀₁	—	2	2	no	—
211	C₂³×C₁₀₁	—	2	2	no	—
212	C₂³×C₁₀₁	—	2	4	no	—
213	C₂³×C₁₀₁	—	2	4	no	—
214	C₂³×C₁₀₁	—	4	2	no	—
215	C₂³×C₁₀₁	—	4	2	no	—
216	C₂³×C₁₀₁	—	4	2	no	—
217	C₂³×C₁₀₁	—	4	2	no	—
218	C₂³×C₁₀₁	—	4	4	no	—
219	C₂³×C₁₀₁	—	4	4	no	—
220	C₂³×C₁₀₁	—	8	8	no	—
221	C₂³×C₁₀₁	—	8	2	no	—
222	C₂³×C₁₀₁	—	8	2	no	—
223	C₂³×C₁₀₁	—	8	8	no	—
224	C₂³×C₁₀₁	—	8	2	no	—
225	C₂³×C₁₀₁	—	8	2	no	—
226	C₂³×C₁₀₁	—	8	2	no	—
227	C₂³×C₁₀₁	—	8	2	no	—
228	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
229	C₂³×C₁₀₁	#121	1	1	yes	characteristic
230	C₂³×C₁₀₁	#121	1	1	yes	characteristic
231	C₂³×C₁₀₁	#123	1	2	yes	—
232	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
233	Q₈×C₁₀₁	—	2	2	no	—
234	Q₈×C₁₀₁	—	2	4	no	—
235	Q₈×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
236	D₄×C₁₀₁	—	2	4	no	—
237	D₄×C₁₀₁	—	2	4	no	—
238	D₄×C₁₀₁	—	2	8	no	—
239	D₄×C₁₀₁	—	2	4	no	—
240	D₄×C₁₀₁	—	2	4	no	—
241	D₄×C₁₀₁	—	2	2	no	—
242	D₄×C₁₀₁	—	2	4	no	—
243	D₄×C₁₀₁	—	4	2	no	—
244	D₄×C₁₀₁	—	4	2	no	—
245	D₄×C₁₀₁	—	4	4	no	—
246	D₄×C₁₀₁	—	4	4	no	—
247	D₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
248	C₂×C₄×C₁₀₁	—	2	2	no	—
249	C₂×C₄×C₁₀₁	—	2	4	no	—
250	C₂×C₄×C₁₀₁	—	2	4	no	—
251	C₂×C₄×C₁₀₁	—	2	4	no	—
252	C₂×C₄×C₁₀₁	—	2	8	no	—
253	C₂×C₄×C₁₀₁	—	4	2	no	—
254	C₂×C₄×C₁₀₁	—	8	2	no	—
255	C₂×C₄×C₁₀₁	—	8	2	no	—
256	C₂×C₄×C₁₀₁	—	8	2	no	—
257	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
259	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
260	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
261	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
262	C₂×C₄×C₁₀₁	#120	1	2	yes	—
263	C₂×C₄×C₁₀₁	#120	1	2	yes	—
264	C₂×C₄×C₁₀₁	#121	1	2	yes	—
265	C₂×C₄×C₁₀₁	#121	1	2	yes	—
266	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
267	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
268	C₂×C₄×C₁₀₁	#123	1	2	yes	—
269	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
275	C₈×C₁₀₁	—	2	4	no	—
276	C₈×C₁₀₁	—	2	2	no	—
277	C₈×C₁₀₁	—	2	4	no	—
278	C₈×C₁₀₁	—	2	2	no	—
279	C₈×C₁₀₁	—	4	2	no	—
280	C₂²×C₁₀₁	—	2	4	no	—
281	C₂²×C₁₀₁	—	2	4	no	—
282	C₂²×C₁₀₁	—	2	1	no	—
283	C₂²×C₁₀₁	—	2	1	no	—
284	C₂²×C₁₀₁	—	2	1	no	—
285	C₂²×C₁₀₁	—	2	1	no	—
286	C₂²×C₁₀₁	—	2	4	no	—
287	C₂²×C₁₀₁	—	4	8	no	—
288	C₂²×C₁₀₁	—	4	2	no	—
289	C₂²×C₁₀₁	—	4	2	no	—
290	C₂²×C₁₀₁	—	4	4	no	—
291	C₂²×C₁₀₁	—	8	4	no	—
292	C₂²×C₁₀₁	—	8	4	no	—
293	C₂²×C₁₀₁	—	8	8	no	—
294	C₂²×C₁₀₁	—	8	8	no	—
295	C₂²×C₁₀₁	—	8	2	no	—
296	C₂²×C₁₀₁	—	8	2	no	—
297	C₂²×C₁₀₁	#386	1	2	yes	—
298	C₂²×C₁₀₁	#386	1	2	yes	—
299	C₂²×C₁₀₁	#471	1	2	yes	—
300	C₂²×C₁₀₁	#472	1	2	yes	—
301	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
303	C₂²×C₁₀₁	C₂×#123	1	1	yes	characteristic
304	C₄×C₁₀₁	—	2	4	no	—
305	C₄×C₁₀₁	—	8	2	no	—
306	C₄×C₁₀₁	#386	1	2	yes	—
307	C₄×C₁₀₁	#386	1	2	yes	—
308	C₄×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
309	C₄×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
310	C₄×C₁₀₁	C₂×#120	1	1	yes	characteristic
311	C₄×C₁₀₁	C₂×#121	1	1	yes	characteristic
312	C₂×#1907	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂×C₁₀₁	—	2	1	no	—
314	C₂×C₁₀₁	—	2	1	no	—
315	C₂×C₁₀₁	—	2	2	no	—
316	C₂×C₁₀₁	—	4	4	no	—
317	C₂×C₁₀₁	—	8	4	no	—
318	C₂×C₁₀₁	#1907	1	4	yes	direct product factor
319	C₂×C₁₀₁	C₂×#386	1	1	yes	characteristic
320	C₂×C₁₀₁	C₂×#471	1	1	yes	characteristic
321	C₂×C₁₀₁	C₂×#472	1	1	yes	characteristic
322	C₂²×AGL(1,ℤ/8)	C₂×C₁₀₁	1	1	yes	characteristic
323	C₂²×#131	C₂×C₁₀₁	1	1	yes	characteristic, complemented
324	C₂×#417	C₂×C₁₀₁	1	1	yes	characteristic, complemented
325	C₂²×#102	C₂×C₁₀₁	1	1	yes	characteristic, complemented
326	C₂²×#100	C₂×C₁₀₁	1	1	yes	characteristic, complemented
327	#1907	C₂×C₁₀₁	1	8	yes	direct product factor
328	C₂×#343	C₂×C₁₀₁	1	1	yes	characteristic, complemented
329	C₂×#341	C₂×C₁₀₁	1	1	yes	characteristic, complemented
330	C₁₀₁	C₂×#1907	1	1	yes	characteristic, direct product factor, Sylow
331	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
332	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
333	C₂×AGL(1,ℤ/8)	—	2	4	no	—
334	C₂×AGL(1,ℤ/8)	—	2	2	no	—
335	C₂×AGL(1,ℤ/8)	C₄×C₁₀₁	1	8	yes	complemented
336	C₂×AGL(1,ℤ/8)	C₂²×C₁₀₁	1	4	yes	—
337	C₂²×SD₁₆	—	2	1	no	—
338	C₂²×D₈	—	2	1	no	—
339	C₂×#131	—	2	4	no	—
340	C₂×#131	—	2	4	no	—
341	C₂×#131	—	2	2	no	—
342	C₂×#131	C₂²×C₁₀₁	1	4	yes	complemented
343	C₂²×M₁₆	—	2	1	no	—
344	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
345	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
346	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
347	C₂³×C₈	—	2	1	no	—
348	C₂³×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
349	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
350	#417	—	2	2	no	—
351	#417	C₂²×C₁₀₁	1	4	yes	complemented
352	C₂×#103	—	2	1	no	—
353	C₂×#102	—	2	1	no	—
354	C₂×#102	—	2	1	no	—
355	C₂×#102	—	2	1	no	—
356	C₂×#102	—	2	2	no	—
357	C₂×#102	C₂²×C₁₀₁	1	4	yes	complemented
358	C₂×#100	—	2	4	no	—
359	C₂×#100	C₂²×C₁₀₁	1	4	yes	complemented
360	#343	C₂²×C₁₀₁	1	4	yes	complemented
361	#341	C₂²×C₁₀₁	1	4	yes	complemented
362	C₂⁵	—	2	1	no	—
363	C₂×#41	—	2	2	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	C₂×C₄×C₁₀₁	1	4	yes	—
368	C₂×#41	D₄×C₁₀₁	1	4	yes	—
369	C₂×#41	D₄×C₁₀₁	1	2	yes	—
370	C₂×#41	C₂³×C₁₀₁	1	2	yes	—
371	C₂²×Q₈	D₄×C₁₀₁	1	1	yes	characteristic
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	—	2	1	no	—
374	C₂²×D₄	—	2	2	no	—
375	C₂²×D₄	—	2	1	no	—
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	2	no	—
379	C₂²×D₄	—	2	2	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
382	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
383	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
387	AGL(1,ℤ/8)	—	2	16	no	—
388	AGL(1,ℤ/8)	—	2	8	no	—
389	AGL(1,ℤ/8)	C₂×C₄×C₁₀₁	1	16	yes	complemented
390	C₂×SD₁₆	—	2	8	no	—
391	C₂×SD₁₆	—	2	4	no	—
392	C₂×D₈	—	2	8	no	—
393	C₂×D₈	—	2	4	no	—
394	#131	—	2	16	no	—
395	#131	—	2	8	no	—
396	#131	—	2	8	no	—
397	C₂×M₁₆	—	2	8	no	—
398	C₂×M₁₆	—	2	2	no	—
399	C₂×M₁₆	—	2	1	no	—
400	C₂×M₁₆	—	2	2	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	—	2	1	no	—
403	C₂×M₁₆	—	2	4	no	—
404	C₂×M₁₆	—	2	2	no	—
405	C₂×M₁₆	—	2	2	no	—
406	C₂×M₁₆	C₂×C₄×C₁₀₁	1	4	yes	—
407	C₂×M₁₆	D₄×C₁₀₁	1	4	yes	—
408	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
409	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
410	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
411	C₂²×C₈	—	2	8	no	—
412	C₂²×C₈	—	2	1	no	—
413	C₂²×C₈	—	2	2	no	—
414	C₂²×C₈	—	2	2	no	—
415	C₂²×C₈	—	2	1	no	—
416	C₂²×C₈	—	2	4	no	—
417	C₂²×C₈	—	2	1	no	—
418	C₂²×C₈	D₄×C₁₀₁	1	1	yes	characteristic
419	C₂²×C₈	D₄×C₁₀₁	1	1	yes	characteristic
420	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
421	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
428	#103	—	2	4	no	—
429	#102	—	2	4	no	—
430	#102	—	2	4	no	—
431	#102	—	2	4	no	—
432	#100	—	2	8	no	—
433	C₂⁴	—	2	1	no	—
434	C₂⁴	—	2	4	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	4	1	no	—
437	C₂⁴	—	4	1	no	—
438	C₂⁴	—	4	2	no	—
439	C₂⁴	—	8	2	no	—
440	C₂⁴	—	8	2	no	—
441	C₂⁴	#41×C₁₀₁	1	1	yes	characteristic
442	#41	—	2	4	no	—
443	#41	—	2	4	no	—
444	#41	—	2	4	no	—
445	#41	—	2	4	no	—
446	#41	—	2	4	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	C₂²⋊C₄×C₁₀₁	1	8	yes	—
450	#41	C₂²×C₄×C₁₀₁	1	4	yes	—
451	#41	C₂×D₄×C₁₀₁	1	4	yes	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	4	yes	—
455	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	—	4	2	no	—
475	C₂×D₄	—	4	2	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
480	C₂×D₄	C₂²×C₄×C₁₀₁	1	4	yes	—
481	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	—	8	2	no	—
491	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
492	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
493	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
498	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
499	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
501	SD₁₆	—	2	16	no	—
502	D₈	—	2	16	no	—
503	M₁₆	—	2	16	no	—
504	M₁₆	—	2	4	no	—
505	M₁₆	—	2	4	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	2	2	no	—
509	M₁₆	—	2	2	no	—
510	M₁₆	—	4	2	no	—
511	M₁₆	C₂²×C₄×C₁₀₁	1	4	yes	—
512	M₁₆	C₂×D₄×C₁₀₁	1	4	yes	—
513	C₂×C₈	—	2	16	no	—
514	C₂×C₈	—	2	4	no	—
515	C₂×C₈	—	2	2	no	—
516	C₂×C₈	—	2	4	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	4	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	4	2	no	—
525	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
526	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	4	2	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	4	4	no	—
541	C₂³	—	4	4	no	—
542	C₂³	—	8	8	no	—
543	C₂³	—	8	2	no	—
544	C₂³	—	8	2	no	—
545	C₂³	—	8	8	no	—
546	C₂³	—	8	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	—	8	2	no	—
549	C₂³	—	8	2	no	—
550	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
551	C₂³	#121×C₁₀₁	1	1	yes	characteristic
552	C₂³	#121×C₁₀₁	1	1	yes	characteristic
553	C₂³	#123×C₁₀₁	1	2	yes	—
554	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	4	no	—
557	Q₈	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
558	D₄	—	2	4	no	—
559	D₄	—	2	4	no	—
560	D₄	—	2	8	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	4	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	4	no	—
568	D₄	—	4	4	no	—
569	D₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	8	2	no	—
579	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
580	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
581	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
582	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
583	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
584	C₂×C₄	#120×C₁₀₁	1	2	yes	—
585	C₂×C₄	#120×C₁₀₁	1	2	yes	—
586	C₂×C₄	#121×C₁₀₁	1	2	yes	—
587	C₂×C₄	#121×C₁₀₁	1	2	yes	—
588	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
589	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
590	C₂×C₄	#123×C₁₀₁	1	2	yes	—
591	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
593	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
596	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
597	C₈	—	2	4	no	—
598	C₈	—	2	2	no	—
599	C₈	—	2	4	no	—
600	C₈	—	2	2	no	—
601	C₈	—	4	2	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	4	8	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	8	4	no	—
614	C₂²	—	8	4	no	—
615	C₂²	—	8	8	no	—
616	C₂²	—	8	8	no	—
617	C₂²	—	8	2	no	—
618	C₂²	—	8	2	no	—
619	C₂²	#386×C₁₀₁	1	2	yes	—
620	C₂²	#386×C₁₀₁	1	2	yes	—
621	C₂²	#471×C₁₀₁	1	2	yes	—
622	C₂²	#472×C₁₀₁	1	2	yes	—
623	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
624	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
625	C₂²	C₂×#123×C₁₀₁	1	1	yes	characteristic
626	C₄	—	2	4	no	—
627	C₄	—	8	2	no	—
628	C₄	#386×C₁₀₁	1	2	yes	—
629	C₄	#386×C₁₀₁	1	2	yes	—
630	C₄	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
631	C₄	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
632	C₄	C₂×#120×C₁₀₁	1	1	yes	characteristic
633	C₄	C₂×#121×C₁₀₁	1	1	yes	characteristic
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	2	no	—
637	C₂	—	4	4	no	—
638	C₂	—	8	4	no	—
639	C₂	C₁₀₁×#1907	1	4	yes	direct product factor
640	C₂	C₂×#386×C₁₀₁	1	1	yes	characteristic
641	C₂	C₂×#471×C₁₀₁	1	1	yes	characteristic
642	C₂	C₂×#472×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#121
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×AGL(1,ℤ/8)×C₁₀₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×#131×C₁₀₁	C₂	semidirect
3. C₂×#417×C₁₀₁	C₂	semidirect
4. C₂²×#102×C₁₀₁	C₂	semidirect
5. C₂²×#100×C₁₀₁	C₂	semidirect
6. C₁₀₁×#1907	C₂	direct (N × H)
7. C₂×#343×C₁₀₁	C₂	semidirect
8. C₂×#341×C₁₀₁	C₂	semidirect
13. C₂×AGL(1,ℤ/8)×C₁₀₁	C₄	semidirect
20. C₂×#131×C₁₀₁	C₂²	semidirect
29. #417×C₁₀₁	C₂²	semidirect
35. C₂×#102×C₁₀₁	C₂²	semidirect
37. C₂×#100×C₁₀₁	C₂²	semidirect
38. #343×C₁₀₁	C₂²	semidirect
39. #341×C₁₀₁	C₂²	semidirect
67. AGL(1,ℤ/8)×C₁₀₁	C₂×C₄	semidirect
312. C₂×#1907	C₁₀₁	direct (N × H)
318. C₂×C₁₀₁	#1907	direct (N × H)
323. C₂²×#131	C₂×C₁₀₁	semidirect
324. C₂×#417	C₂×C₁₀₁	semidirect
325. C₂²×#102	C₂×C₁₀₁	semidirect
326. C₂²×#100	C₂×C₁₀₁	semidirect
327. #1907	C₂×C₁₀₁	direct (N × H)
328. C₂×#343	C₂×C₁₀₁	semidirect
329. C₂×#341	C₂×C₁₀₁	semidirect
330. C₁₀₁	C₂×#1907	direct (N × H)
335. C₂×AGL(1,ℤ/8)	C₄×C₁₀₁	semidirect
342. C₂×#131	C₂²×C₁₀₁	semidirect
351. #417	C₂²×C₁₀₁	semidirect
357. C₂×#102	C₂²×C₁₀₁	semidirect
359. C₂×#100	C₂²×C₁₀₁	semidirect
360. #343	C₂²×C₁₀₁	semidirect
361. #341	C₂²×C₁₀₁	semidirect
389. AGL(1,ℤ/8)	C₂×C₄×C₁₀₁	semidirect
639. C₂	C₁₀₁×#1907	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×AGL(1,ℤ/8)×C₁₀₁	2
C₂²×#131×C₁₀₁	2
C₂×#417×C₁₀₁	2
C₂²×#102×C₁₀₁	2
C₂²×#100×C₁₀₁	2
C₁₀₁×#1907	2
C₂×#343×C₁₀₁	2
C₂×#341×C₁₀₁	2
C₂×#1907	101

Subgroups — C2×C101×#1907 #38803152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1907 #38803152